Vectors and motion in 2-D Adding vectors to find total displacement Method 1: Graphical addition: Tail of next vector on tip of previous

Method 2: Adding x and y components Adding vectors to find total displacement Method 2: Adding x and y components SP 1.8

Method 2: Adding x and y components Add components Adding vectors to find total displacement Method 2: Adding x and y components Add components Find total’s magnitude from Find angle from some axis from SP 1.8

A few graphical exercises P1. Draw A+B, and choose quadrant: P2. Draw B-A, and choose quadrant P3. Draw 2A – ½B, and choose quadrant

Relative velocity in 2-D

If the plane points E, and the wind is S, how will the plane move over the ground? vPG = vPA + vAG

If the vectors aren’t perpendicular… add the components 200 50 vPG = vPA + vAG vPG = vPA + vAG

Math: vPG = vPA + vAG can be written: v­PA = v­PG + - vAG If the wind is to the S at 90 km/hr, in what direction must a plane flying 500 km/hr airspeed point itself in order to fly exactly E? Concept: the plane must have part of its v going “upwind” to exactly cancel the effect of the wind; the rest of its v points in the direction you want to go over the ground. Math: vPG = vPA + vAG can be written: v­PA = v­PG + - vAG -vAG

An ocean has a 10 mph current to the southwest An ocean has a 10 mph current to the southwest. If a boat wishes to sail at 20 mph north vs the ground (or GPS), what direction should the boat point?

HW2: An airplane is flying in a jet stream that is blowing at 45 HW2: An airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 20º south of east. Its direction of motion relative to the Earth is 45.0º south of west, while its direction of travel relative to the air is 5.00º south of west. Sketch the three vectors and label the known triangle lengths and angles.

Lecture 2, HW2 Vectors Basic concepts: Basic problems: adding two vectors graphically Basic problems: adding two perpendicular vectors with Pythagorean them, including for relative velocity finding components of vectors finding angle and magnitudes from components Advanced problems: adding, subtracting vectors with components relative velocity with non-perpendicular vectors

Concept review Which of the following graphs represents 1. a bike moving at constant velocity 2. a car speeding up then slowing down 3. a ball thrown up in the air that comes back down 4. a car that always speeds up 5. a motorcycle that slows down and parks. Careful! a, b are velocity v(t), and the others are position x(t)